# Category:Definitions/Regular Representations

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This category contains definitions related to Regular Representations.

Related results can be found in **Category:Regular Representations**.

Let $\struct {S, \circ}$ be a magma.

### Left Regular Representation

The mapping $\lambda_a: S \to S$ is defined as:

- $\forall x \in S: \map {\lambda_a} x = a \circ x$

This is known as the **left regular representation of $\struct {S, \circ}$ with respect to $a$**.

### Right Regular Representation

The mapping $\rho_a: S \to S$ is defined as:

- $\forall x \in S: \map {\rho_a} x = x \circ a$

This is known as the **right regular representation of $\struct {S, \circ}$ with respect to $a$**.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Definitions/Regular Representations"

The following 6 pages are in this category, out of 6 total.